The latest news is that the BA gearbox from my Square Four is now stripped and washed out. If you recall, some dogs were clattering at idle, in neutral.
For the record, there's 0.88 mm (35 thou or just over 1/32") end float on the main shaft and about 0.23 mm (9 thou) on the layshaft and selector. I've improved these numbers from my previous post by fixing the DTI more securely. There's no gasket fitted between the inner cover and the shell.
The worst damage I have seen is on the layshaft clutch first gear dogs and the layshaft first gear. This is always noisy going in; my clutch basket isn't brilliant and I have a new one to go in. The clutch drags when hot and I think that's what causes this damage.
The selector forks are straight and have a nice sliding fit, minimal play, in the mainshaft sliding gear and the layshaft clutch:
Here's a video looking at all the gears:
As to the rattling/clattering at idle, I'm not sure. There's a lot of end float in the layshaft and selector shaft (Waller says 1-2 thou minimum but doesn't define a maximum) which could give rise to this clattering -particularly if one shaft goes one way and one the other, but although the mainshaft float is at the end of it's limit I can't see how that would cause the noise.
Grateful as always for your advice!